Question 460447
<pre>

>>...The number of dimes is three more than the number of nickels...<<

                       d = n + 3

>>...the number of quarters is four less than the number of nickels...<<

                       q = n - 4

>>...the value of the coins is less than $10,...<< 

$0.05n + $0.10d + $0.25q < $10.00

Multiply that by 100 and drop $ marka:

          5n + 10d + 25q < 1000

Divide through by 5

             n + 2d + 5q < 200

Substitute d = n + 3 and q = n - 4

 n + 2(n + 3) + 5(n - 4) < 200

    n + 2n + 6 + 5n - 20 < 200

                 8n - 14 < 200

                      8n < 214
                       
                       n < 26.75

        
The answer is 26 nickels. for that is the largest whole number
that does not exceed 26.75

In fact the maximum number of dimes, the maximum number of
nickels, and the maximum number of quarters are all three
achieved if the piggy bank contains $9.70 with 29 dimes, 
26 nickels and 22 quarters.

Edwin</pre>